Demonstrators gathered in the streets of Phoenix, Arizona, Thursday to protest the state's new illegal immigration law. The demonstrations came on the heels of a federal judge's decision to block most of the key measures in the law. At least 50 activists protesting the law were arrested outside the Maricopa County jail in downtown Phoenix.

PHOENIX -- The showdown over Arizona's immigration law played out in court and on Phoenix's sun-splashed streets on Thursday, as the state sought to reinstate key parts of the measure and angry protesters chanted that they refused to "live in fear." Dozens were arrested.

A federal judge's decision a day earlier to block the strict law's most controversial elements didn't dampen the raging immigration debate.

The judge has been threatened. Protesters rallied in cities from Los Angeles to New York. The sheriff of the state's most populous county vowed to continue targeting illegal immigrants. Lawmakers or candidates in as many as 18 states say they still want to push similar measures.

Along the U.S.-Mexico border, life continued as before, with officials sending back people who were captured while attempting to cross.

In Phoenix, hundreds of the law's opponents massed at a downtown jail, beating on the metal door and forcing sheriff's deputies to call for backup. Officers arrested at least 32 people, and dozens more were detained elsewhere throughout the day.

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Activists focused their rage at Maricopa County Sheriff Joe Arpaio, the 78-year-old ex-federal drug agent known for his immigration sweeps.

Outside his downtown office, marchers chanted "Sheriff Joe, we are here. We will not live in fear." One was dressed in a papier-mFache "Sheriff Joe" head and prison garb. Arpaio said he'd continue with a Thursday sweep.

"I'm not going to be intimidated and stopped," he said. "If I have to go out and get in the car, I'll do it."

Activists, armed with video cameras and aided by others listening to police scanners, roamed the county's neighborhoods, saying they were ready to document any deputies harassing Hispanics.

In Tucson, between 50 and 100 people on both sides of the issue gathered at a street corner. About 200 protesters blocked a busy Los Angeles intersection, with police arrested about a dozen who were linked with plastic pipes and chains.

In New York, about 300 immigrant advocates rallied near the federal courthouse in lower Manhattan.

In Los Angeles police have arrested 10 people who blocked an intersection to protest Arizona's new immigration law. About 200 protesters gathered at a busy intersection west of downtown.

"It's one step closer for us, but I think the fight is still ahead," said Adelfa Lugo, a 56-year-old Mexican-born Brooklyn resident who joined the protest. "If we don't fight this in Arizona, this anti-immigrant feeling will spread across the country."

Since Wednesday's ruling, U.S. District Judge Susan Bolton has received thousands of phone calls and e-mails. Some were positive, but others were "from people venting and who have expressed their displeasure in a perverted way," said David Gonzales, the U.S. Marshal for Arizona.

Gonzales said his agents are taking some of the threats to Bolton seriously. He wouldn't say how many there were or whether any threats were coming from recognized hate groups. He refused to discuss any extra security measures, which U.S. marshals routinely provide federal judges.

The protests came as Gov. Jan Brewer appealed Bolton's ruling to the 9th U.S. Circuit Court of Appeals in San Francisco.

The governor, who hired lawyers to defend the law in court, hopes the court will act quickly, saying illegal immigration remains an ongoing crisis.

Arizona has more than 400,000 illegal immigrants, and its border with Mexico is awash with smugglers who funnel narcotics and immigrants throughout the U.S. The law's supporters say the influx of illegal migrants drains vast sums of money from hospitals, education and other services.

The Obama administration has decided to send National Guard troops to the border states to help federal agents with security.

Along the U.S.-Mexico border in punishing temperatures of more than 100 degrees Thursday, two immigrants climbed a fence and fled on foot, while a third threw rocks in the direction of Border Patrol agents. The officers arrested them. New deportees congregated around Nogales.

The Arizona National Guard officials say they hope to have 524 troops in place by the end of September. Troops are expected to arrive at the border in New Mexico and Texas by mid-August, and California officials have estimated an Oct. 1 deadline to have troops fully deployed there.

In Phoenix, demonstrators had promised nonviolent civil disobedience, and they gathered in front of the sheriff's office by the hundreds, blocking traffic and swarming around several cars caught in the protest.

Police moved in to try to allow the drivers to leave, as the crowd shouted, "We will not comply."

Over the next hour, the crowd surged, chanted, yelled and some protesters forced the arrests. They then moved on the to jail.

As Arpaio held a news conference, he got a telephone call, and he told the caller: "OK, we're going to divert our deputies down in front of the jail ... What you do, anybody that resists, you put 'em in our jail. We're going to lock 'em up."

Then he turned to reporters: "As I said, we're not going to allow our jails to be held hostage by these activists, so they're going to jail.

"And if we have to put 200 in there, that's where they're going," he said, adding that the sweeps would continue.

During the sweeps, deputies usually flood an area of a city -- in some cases heavily Latino areas -- to seek out traffic violators and arrest other alleged lawbreakers. Sixty percent of the nearly 1,000 people arrested in the sweeps since early 2008 have been illegal immigrants.

The Justice Department launched an investigation of his office nearly 17 months ago over allegations of discrimination and unconstitutional searches and seizures. Although the department has declined to detail its investigation, Arpaio believes it centers on his sweeps.

The agency's civil rights attorneys and investigators were in Phoenix Thursday as part of their probe, DOJ spokeswoman Xochitl Hinojosa said. She declined to comment on the status of the inquiry or answer any other questions.

In October 2009, when the federal government stripped Arpaio of his power to let 100 deputies make federal immigration arrests, he launched another sweep the next day.

Unable to make arrests under a federal statute, the sheriff instead relied on a nearly 5-year-old state law that prohibits immigrant smuggling.

The elements of the new law that took effect on Thursday will likely aid Arpaio in his immigration efforts.

In her temporary injunction, Bolton delayed the most contentious provisions of the law, including a section that required officers to check a person's immigration status while enforcing other laws.

Bolton indicated the federal government's case has a good chance at succeeding in its argument that federal immigration law trumps state law.

But she allowed police to enforce the law's bans on blocking vehicle traffic when seeking or offering day-labor services and a revision to the smuggling ban that lets officers stop drivers if they suspect motorists have broken traffic laws.

Bolton also let officers enforce a new prohibition on driving or harboring illegal immigrants in furtherance of their illegal presence.

Opponents of the law said the ruling sends a strong message to other states hoping to replicate the law.

But a Republican lawmaker in Utah said the state will likely take up a similar law anyway when their legislative sessions start up again in 2011.

"The ruling ... should not be a reason for Utah to not move forward," Utah state Rep. Carl Wimmer said.